Currently, a concentrated photovoltaic (CPV) sun tracking system requires high accuracy sun tracking. If the sun tracking angle deviates slightly, the output power drops abruptly. There are three following main control modes for current dual-axis sun trackers:
1. A closed loop dual-axis sun tracker uses a light sensor to track the sun's position and outputs signals to drive an azimuth motor and an elevation motor so as to achieve the function of tracking the sun. However, its tracking accuracy is affected by the sensitivity of the light sensor and the weather.
2. An open loop dual-axis sun tracker calculates the position of the sun and outputs theoretical value signals obtained from the calculation results to drive an azimuth motor and an elevation motor so as to achieve the function of tracking the sun. However, its tracking accuracy is affected by calculation formulae, assembly errors of the tracker and motor control, etc.
3. A hybrid mode dual-axis sun tracker uses a light sensor to track the sun's position. When in bad weather, the sun tracker is switched to the open loop mode, or tracks over a wide range in the open loop mode and then tracks over a narrow range in the closed loop mode.
The first and third modes require the use of a light sensor. Although they can achieve high accuracy sun tracking, the weather, the stained or damaged surface, or the like can easily cause deviation in tracking the sun. The open loop dual-axis sun tracker does not require the use of a light sensor and can stably track the sun without the influence of the external environment. However, other factors such as assembly errors generated when the tracker is assembled and mounted, deflection of incident sunlight into the atmosphere or accuracy of the sun position calculation program can cause deviation in tracking the sun.
Current celestial body trackers (e.g., astronomical telescopes, sun trackers) have pointing deviation problems similar to those described above. A current solution applied to astronomical telescopes uses a pointing error model to perform pointing correction. However, similar pointing correction technology is infrequent in sun trackers so that sun-tracking accuracy of open loop systems is poor.
An error model is a mathematical expression that simulates pointing deviation, whereby pointing deviation data is analyzed to obtain various pointing deviation factors of a tracker and to further correct the pointing deviation accordingly. The current error model applied to astronomical telescopes is proposed by Stumpff (1972) and Ulich (1981). The correcting method of the proposed model for an example is briefly described as follows:ΔA=IA+CA sec(E)+NPAE tan(E)+AN tan(E)sin(A)−AW tan(E)cos(A)+Aobs sec(E)  (1)ΔE=IE+ECEC cos(E)+AN cos(A)+AW sin(A)+Eobs+R(Ps,Ts,RH,E)  (2)where A is the azimuth, E is the elevation, in the phase of pointing error data collection, ΔA represents the azimuth deviation, ΔE represents the elevation deviation, but in the phase of pointing correction, ΔA represents the azimuth correction command, ΔE represents the elevation correction command, which are combined with the azimuth A and the elevation E to form correction commands A′=A+ΔA and E′=E+ΔE, which are inputted into the tracker to correct the original pointing deviation.
Each coefficient in the above-mentioned pointing error model represents as follows:
IA: the azimuth axis zero offset;
IE: the elevation axis zero offset;
AN: the azimuth axis offset/misalignment north-south;
AW: the azimuth axis offset/misalignment east-west;
NPAE: Non-perpendicularity between the mount azimuth and elevation axes;
CA: the collimation error of the optical element;
ECEC: the gravitational flexure correction at the horizon;
R (Ps, Ts, RH, E): the atmospheric refraction correction (Ps is the barometric pressure, Ts is the temperature, and RH is the relative humidity);
Aobs: the observer-applied azimuth correction; and
Eobs: the observer-applied elevation correction.
The correcting procedure using the conventional pointing error model comprises the following steps: observing the structure of a tracker, establishing the corresponding pointing error model through mathematical derivation; measuring pointing deviation data of the celestial body tracker, combining the azimuth A and the elevation E with the azimuth deviation ΔA, and the elevation deviation ΔE measured at the same time as a data set, wherein the number of data sets must be greater than the number of error model coefficients; inputting the data sets into the pointing error model analysis program, performing curve fitting analysis by using the QR decomposition method to obtain the pointing error model coefficients; inputting the pointing error model coefficients into the pointing control program of the tracker to complete pointing correction.
However, for the simplification of algorithmic requirements, the conventional error model assumes that all the deviations and the azimuth deviations and elevation deviations resulted from various error factors are small angles (<2°). Therefore, a small angle approximation method (for example, sin θ˜θ) can be employed to simplify the mathematical derivation procedures, but it also limits the pointing deviation correction function of the pointing error model. For example, at summer noon in Taiwan, the position of the sun is very close to the pole of horizontal celestial coordinate system (zenith, at an elevation of 90°). Therefore, as shown in FIG. 1, the tracker cannot accurately point toward the sun after corrected by the pointing error model (S indicates the path of the sun, E indicates the path before the tracker is corrected, and C indicates the path after the tracker is corrected). Nonetheless, summer is the season of the maximum sunshine amount in a whole year, so an attempt should be made to analyze and solve such problem. In addition, the actual pointing deviation near the pole is far less than the azimuth deviation, but the special characteristics of azimuth dimensions in a horizontal celestial coordinate system are that all of them converge at the zenith to form the pole of the coordinate system. Namely, the azimuth values vary severely near the pole. Therefore, even if the pointing deviation is small, a very large azimuth deviation will be resulted from the characteristics of such coordinate system.
U.S. Pat. No. 6,704,607 discloses a pointing error correcting method for an open loop sun tracking system using an error model. The error model coefficients are coupled with each other, so these error model coefficients representing various errors must be solved in a predetermined order. The deviation data inputted for error model analysis must have azimuthal symmetry to satisfy the assumption in the derivation of this error model. When a new error factor of the tracker is found through the observation of the deviation data, it is necessary to derive various error model functions again. This method is more limited and more complicated.